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Structural and kinetic studies of crystallization of Te51As42Cu7 chalcogenide glass
Journal of Alloys and Compounds 486 (2009) 97–102
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Structural and kinetic studies of crystallization of Te51 As42 Cu7 chalcogenide glass A.A. Abu-Sehly ∗,1 Physics Department, Faculty of Science, Taibah University, PO Box 344, Madina, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 9 May 2009 Received in revised form 17 June 2009 Accepted 18 June 2009 Available online 25 June 2009 PACS: 6470.P 6140 6140.D
a b s t r a c t Differential scanning calorimetry (DSC) technique was used to investigate the kinetics of crystallization in Te51 As42 Cu7 chalcogenide glass. Non-isothermal measurements were performed at different heating rates (2–99 K min−1 ). Two exothermic peaks were observed reflecting the presence of multiple phases in agreement with the structural investigation. A strong heating rate dependence of the activation energies associated with the two peaks was observed when the data were analyzed using Matusita model. This variation of the activation energy was confirmed by the application of the different isoconversional methods. These methods showed that the activation energy of crystallization is not constant but varies with temperature. Different temperature dependence of the activation energy was observed for the two crystallization peaks. © 2009 Elsevier B.V. All rights reserved.
Keywords: DSC Crystallization kinetics Chalcogenide glass Activation energy Isoconversional methods
1. Introduction Chalcogenide glasses have drawn a great attention during the last years. This is due to the fact that some amorphous materials show certain unusual switching properties that could be important in modern technological applications such as switching, electrophotography, and memory devices [1–4]. The system Te–As–Cu attracted considerable attention in the past because of the fact that addition of d-elements, such as Cu, to the chalcogenide glasses causes significant changes in their properties. This may reflect positively on their technological applications. The study of crystallization kinetics in amorphous materials by DSC methods has been discussed in many literatures [5–10]. There are several theoretical models and equations suggested to explain the crystallization kinetics. These models and equations will also be used for this study. Isoconversion methods are widely used to obtain reliable and consistent kinetic information from non-isothermal data. They can reveal the complexity of multiple reactions due to the dependence of the activation energy on the extent of conversion [10–14]. The kinetics of crystallization can be described by the following rate equation assuming Arrhenius temperature dependence of the
∗ Tel.: +966 508629110; fax: +966 48454770. E-mail address: [email protected]. 1 On leave from Physics Dept., Assiut University, Assiut, Egypt. 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.06.119
rate constant [14,15]:
d˛ E = A exp − RT dt
f (˛),
(1)
where t is the time, T is the temperature, ˛ is the conversion fraction that represents the volume of the crystallized fraction, A (s−1 ) is the pre-exponential (frequency) factor, E (kJ mol−1 ) is the activation energy, R is the universal gas constant, and f(˛) is the reaction model. Under non-isothermal conditions with a constant heating rate of ˇ = dT/dt, Eq. (1) may be rewritten as: d˛ d˛ = dT dt
1 ˇ
=
A E exp − RT ˇ
f (˛).
(2)
For various heating rates, ˇi , the Friedman method [16] can be obtained directly from Eq. (1) at a specific crystallization fraction, ˛, as: ln
d˛ dt
˛i
= CF (˛) −
E˛ , RT˛i
(3)
where the subscript i denotes different heating rates and the parameter CF (˛) = ln(A˛ f(˛)). For a specific ˛ value and several heating rates ˇi , pairs of (d˛/dt)˛i and T˛i are determined experimentally from the DSC thermograph. The parameters E˛ and CF (˛), at this specific value of ˛, are then estimated from a plot of ln(d˛/dt)˛i versus 1/T˛i (Eq. (3)) across at least three different heating rates. The procedure is repeated for many values of ˛, yielding continuous functions of ˛ for E˛ and CF (˛).
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Eq. (2) can be integrated by separation of variables [17,18]:
˛
d˛ A = f (˛) ˇ
0
T
exp − T0
E RT
dT ≈
AE ˇR
0
T
exp(−y) dy, y2
(4)
where T0 is an initial temperature, y = E/RT and T is the temperature at an equivalent (fixed) state of transformation. The integral on the right hand side is usually called the temperature integral, P(y), and does not have analytical solution:
∞
exp(−y) dy. y2
P(y) = yf
(5)
To solve the temperature integral, several approximations were introduced. In general, all of these approximations lead to a direct isoconversion method in the form of
ln
ˇ
Tk
=C−
E . RT
(6)
For each degree of the conversion fraction, ˛, a corresponding k ) against 1/T . The T˛i and heating rate are used to plot ln(ˇi /T˛i ˛i activation energy, E˛ , is then determined from the regression slope. The most popular models used for calculation of activation energy are: (1) The Kissinger–Akahira–Sunose (KAS) method [19–21], which takes the form:
ln
ˇi
= CK (˛) −
2 T˛i
E˛ . RT˛i
E˛ , ln ˇi = CW (˛) − 1.0518 RT˛i
(8)
ln
1.894661 T˛i
E˛ = CT (˛) − 1.00145033 , RT˛i
(9)
(4) The Starink method [13,17], another new method, which is given by:
ln
ˇi 1.92 T˛i
= CS (˛) − 1.0008
˝=
n n I(E˛ , T˛i )ˇj i=1 j = / i
and
I(E˛ , T˛j )ˇi
I(E˛ , T˛i ) =
T˛i
exp 0
(3) The Tang method. A more precise formula for the temperature integral has been suggested by Tang et al. [24], which can be put in the form: ˇi
The third approach of extracting the same information is by using the advanced isoconversional method developed by Vyazovkin [14,25–27]. For a set of n experiments carried out at different heating rates, the activation energy can be determined at any particular value of ˛ by finding the value of E˛ which minimizes the objective function ˝, where:
(7)
(2) The Flynn–Wall–Ozawa (FWO) method, suggested independently by Flynn and Wall [22] and Ozawa [23]. This method is given by:
Fig. 2. Typical DSC trace of the Te51 As42 Cu7 chalcogenide glass heated at a constant rate of 15 K min−1 . The separation process for the first (P1) and second (P2) peaks was performed using Gaussian fit.
E˛ , RT˛i
Fig. 1. EDX results of the Te51 As42 Cu7 chalcogenide glass.
,
(11)
−E ˛
RT
dT.
(12)
The temperature integral, I, was evaluated using an approximation suggested by Gorbachev [28]:
T
exp 0
−E RT
dT =
RT 2 E
1 1 + (2RT/E)
exp
−E RT
.
(13)
The present study is concerned with the crystallization kinetics and the effect of temperature on the activation energy of Te51 As42 Cu7 chalcogenide glass by means of isoconversion meth-
(10)
Fig. 3. The XRD patterns of the as-prepared sample and of the annealed samples at different annealing temperature, Ta .
A.A. Abu-Sehly / Journal of Alloys and Compounds 486 (2009) 97–102
99
temperature and enthalpy calibrations were checked with indium (Tm = 429.75 K, Hm = 28.55 J g−1 ) and tin (Tm = 504.97 K, Hm = 59.56 J g−1 ) as a standard material. The structure of the samples was examined using a Shimadzu XRD-6000 Xray diffractometer using CuK˛ radiation ( = 1.5418 Å). The X-ray tube voltage and current were 40 kV and 30 mA, respectively. The X-ray diffractometer was equipped with oven-chamber (Anton Paar HTK 1200N). The measurements were obtained at the annealing temperature. The surface microstructure was revealed by SEM (Shimadzu Superscan SSX-550), and the composition of the alloy was checked by EDX.
3. Results and discussion 3.1. Structural studies
Fig. 4. Electron microscopy patterns of Te51 As42 Cu7 chalcogenide glass as prepared in bulk specimen.
ods. The effect of annealing on the structure of the present sample was also investigated by SEM as well as by X-ray diffraction. 2. Experimental methods Bulk material was prepared by the well-established melt-quench technique. High purity (99.999%) Te, As and Cu in appropriate atomic percentage proportions were weighed and sealed in a quartz glass ampoule under a vacuum of 10−4 Torr. The contents were heated to about 1250 K for 36 h. During the melt process, the tube was frequently shaken to homogenize the resulting alloy. The melt was quenched in ice water to obtain the material in a glassy state. The DSC experiments presented in this paper were performed using a Shimadzu DSC-60 instrument with an accuracy of ±0.1 K, under dry nitrogen supplied at a rate of 35 ml min−1 . The samples were encapsulated in standard aluminum sample pans. To minimize the temperature gradients, the samples were well granulated to form a uniform fine powder and spread as thinly as possible across the bottom of the sample pan. The weight of the sample was kept very small (2–3 mg). Non-isothermal DSC curves were obtained at selected heating rates (ˇ in the range 2–99 K min−1 ). The
Qualitative and quantitative calculations were performed using the EDX technique accomplished with SEM from the displayed characteristic X-ray pattern. The results obtained are shown in Fig. 1. The atomic percentage ratios of Te, As and Cu were found to be 51%, 42% and 7%, respectively. Typical (DSC) curve is shown in Fig. 2. Two exothermic changes were observed: the first one (P1) was between 442 and 491 K for heating rates of 2–99 K min−1 , and the second (P2) from 493 to 534 K for the same heating rate range. The transformation from the amorphous to the crystalline state was investigated by X-ray diffraction measurements performed on sample heated at various temperatures 442, 468, 493, 513, 543 and 563 K. The XRD patterns are shown in Fig. 3. The as prepared sample was amorphous, as shown in Fig. 3. As the temperature increases the sharpness of the lines increases, indicating grain growth. The presence of a (1 1 2) as a main peak at 2 = 29.4◦ could be attributed to As2 Te3 [JCPDS file 75-1470]. There is a gradual phase change as the temperature goes up, but a remarkable change occurred at annealing temperature of 543 K where the peak (1 1 2) at 2 = 29.4◦ nearly disappeared and the peak (1 3 0) at 2 = 27.4◦ which could be attributed to Cu0.656 Te0.344 become the main peak [JCPDS file 37-1026]. The two binary crystalline phases Cu–Te and Cu–As were recognized at high temperatures as reported in our previous study
Fig. 5. Electron microscopy patterns of Te51 As42 Cu7 chalcogenide glass annealed for 15 min at different temperatures. (a) Annealed at 442 K, (b) annealed at 493 K, and (c and d) annealed at 513 K.
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[5], but with less broad composition ranges. The presence of the two peaks at 2 = 39.9◦ and 42.8◦ could be attributed to Cu2 Te[JCPDS files 45-1279 and 06-0649]. An evidence for the binary crystalline phase Cu–As is the presence of the peak at 2 = 37.9◦ which could be attributed to Cu9.5 As4 [JCPDS file 21-0280]. The transformation from the amorphous to the crystalline state was investigated by studying the morphology of the samples. The change in the morphology under isothermal annealing was recorded by SEM. Fig. 4 shows an SEM image of a fractured, as prepared, bulk specimen of Te51 As42 Cu7 . The micrograph shows the conchoidal contours, which are a good indication for glass structure. On the other hand, Fig. 5a–d shows the effect of heat treatments on the morphology under nitrogen flow. Fig. 5a shows an SEM micrograph of the Te51 As42 Cu7 sample after annealing for 15 min at 442 K. The micrograph indicates that the glass structure was distorted by the beginning of crystallization. It shows that the specimen consists of indistinct crystallites embedded in the original amorphous matrix. This distortion dramatically increases as temperature increases as shown in Fig. 5b for a sample annealed at 493 K for 15 min. By increasing the annealing temperature to 513 K for 15 min, a remarkable another phase of crystallization was developed. The crystalline phase appeared as an ordered pattern of very fine structure as shown in Fig. 5c and d. 3.2. The activation energy of crystallization The routinely and most widely used model is the Johnson–Mehl–Avrami (JMA) model for non-isothermal kinetics. This model implies that the Avrami exponent, n, and the activation energy, E, should be constant during the transformation process. Recent papers in this field have shown that n and E are not necessarily constants, but vary during the transformation [5,8–10]. The first step used in the calculation of the activation energy for crystallization is the separation of the processes for the first (P1) and second (P2) peaks by Gaussian fit as shown in Fig. 2. After this, each peak was treated individually. 3.2.1. Evaluation of the activation energy by the JMA model The kinetics of crystallization were obtained using a method specifically suggested for non-isothermal conditions by Matusita et al. [29] as: ln[− ln(1 − ˛)] = −n ln ˇ − 1.052
mE + constant, RT
(14)
where m is an integer which depends on the dimensionality of the crystal, and n is a numerical factor (the Avrami exponent) which also depends on the nucleation process. When the nuclei formed during the heating at a constant rate dominate, n = m + 1 and when nuclei formed during any previous heat treatment prior to thermal analysis are dominant, n = m [8]. In this work the values of the indices n and m are considered to be equal because the sample was pre-annealed for a period of time before each experimental run at a temperature below the glass transition temperature, Tg , thus ensuring that the site was saturated. The plot of ln[−ln(1 − ˛)] against 103 /T is shown in Fig. 6a and b. For both two peaks (P1) and (P2), the resulting straight lines in Fig. 6a and b have slopes that vary gradually with the heating rate. If the crystallization fraction, ˛, is determined at a fixed temperature, at different heating rates, then the Avrami exponent n can be obtained from the slope of the following equation [30]:
d{ln[− ln(1 − ˛)]} = −n. d(ln ˇ) T
(15)
The results are shown in Fig. 7a and b. The calculated values of n were not integers and varied with temperature as shown in Fig. 8. It is worth noting that for P1 the value of n is constant (n ≈ 1) for
Fig. 6. (a) ln[−ln(1 − ˛)] versus 1/T plot at different heating rates for the first peak (P1) of the Te51 As42 Cu7 chalcogenide glass. (b) ln[−ln(1 − ˛)] versus 1/T plot at different heating rates for the second peak (P2) of the Te51 As42 Cu7 chalcogenide glass.
temperatures up to 480 K indicating that the crystallization is dominated by surface morphology. The gradual increase of the values of n for P2 is an indication of changing morphology of the crystallization process from surface (n = 1) to layer (n = 2) structures. This change of morphology with temperature is also evident from Fig. 5b and c, respectively. Fig. 9 shows the variation of the activation energy for crystallization with the heating rate for an average value of n = 1.11 and 1.38 for P1 and P2, respectively obtained from the results. The results show that the activation energy decreases with heating rate more rapidly for P1 than P2. 3.2.2. Evaluation of the activation energy by isoconversional methods The first step in the evaluation of the activation energy for crystallization, E˛ (T), is to apply the isoconversional methods mentioned in Eqs. (3) and (7)–(11) to the overall crystallization data to obtain the dependence of E˛ (T) on ˛ for all heating rates applied. The dependence of E˛ on the temperature can be obtained [15] by replacing ˛ with the respective temperature interval. Fig. 10 shows the dependence of E˛ on the volume fraction crystallized, ˛, for P1 and P2 transformations. The results are obtained by applying the six isoconversional methods of Friedman, KAS, FWO, Tang, Starink and Vyazovkin given in Eqs. (3) and (7)–(11), respectively. The results obtained by the KAS, FWO, Tang, Starink and Vyazovkin methods were well matched and gave identical values while the results obtained by the Friedman method gave dif-
A.A. Abu-Sehly / Journal of Alloys and Compounds 486 (2009) 97–102
101
Fig. 9. Effective activation energy (E) as a function of heating rate for the two crystallization peaks of the Te51 As42 Cu7 chalcogenide glass.
Fig. 7. (a) ln[−ln(1 − ˛)] versus ln(ˇ) plot at different temperatures for the first peak (P1) of the Te51 As42 Cu7 chalcogenide glass. (b) ln[−ln(1 − ˛)] versus ln(ˇ) plot at different temperatures for the second peak (P2) of the Te51 As42 Cu7 chalcogenide glass.
Fig. 10. Dependence of the activation energy for crystallization, E, on the volume of the crystallized fraction, ˛, for the two crystallization peaks.
ferent values. This shift is known and has been discussed for other compounds [9,15]. For P1 the results show that E˛ first decreases rapidly with the extent of conversion, ˛, then, in the conversion range of ˛ > 0.9, E˛ increases for results obtained by Eqs. (7)–(11). Friedman method showed that E˛ started to increase more earlier with the extent
of conversion, at ˛ > 0.7. For P2 the results show that E˛ is nearly constant with the extent of conversion, ˛, with exception at the beginning of crystallization (˛ < 0.2) where E˛ is decreasing. The occurrence of the dependence of E˛ on the volume of the crystallized fraction instantly suggests that the data under study follow
Fig. 8. The variation of the Avrami exponent, n, with temperature for the two crystallization peaks.
Fig. 11. Dependence of the activation energy for crystallization, E, on temperature for the two crystallization peaks.
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A.A. Abu-Sehly / Journal of Alloys and Compounds 486 (2009) 97–102
a multi-step kinetics reaction for P1, while mainly they follow a single-step kinetics reaction for P2. The resulting E˛ (T) dependence as obtained from Eqs. (3) and (7)–(11) is displayed in Fig. 11 for both peaks P1 and P2. For P1 the values of E˛ are positive and decrease with temperature for the six methods used, which simply indicates that the crystallization rate increases as the temperature increases. This behavior demonstrates that the rate of crystallization is, in fact, determined by the rates of the nucleation and diffusion processes [13]. Because these two mechanisms are likely to have different activation energies, the effective activation energy of the transformation will vary with temperature [30]. This interpretation is based on the nucleation theory proposed by Fisher and Turnball [31]. 4. Conclusion The structure and kinetics of crystallization of Te51 As42 Cu7 were investigated. The X-ray diffraction measurements confirmed the presence of different phases as the samples were annealed at different temperature. Different crystalline structures can also be seen from the morphology of specimens annealed at selected stages of heat treatments. Two exothermic peaks were observed reflecting the presence of multiple phases in agreement with the structural results. The activation energies of crystallization, E(T), were estimated by applying different isoconversional methods and were found to be strongly temperature dependent. The results showed a decrease followed by an increase in E(T) with increasing temperature for P1, while for P2, it increases with increasing temperature then followed by a decrease. The observed temperature dependence of E can be understood on the light of the nucleation theory of Fisher and Turnball.
References [1] T. Ohta, J. Optoelectron. Adv. Mater. 3 (2001) 609. [2] S.A. Khan, M. Zulfequar, M. Husain, J. Phys. Chem. Solids 63 (2002) 1787. [3] M. Popescu, J. Optoelectron. Adv. Mater. 7 (2005) 2189. [4] N. Mehta, J. Sci. Ind. Res. 65 (2006) 777. [5] A.A. Joraid, A.A. Abu-Sehly, M. Abu El-Oyoun, S.N. Alamri, Thermochim. Acta 470 (2008) 98. [6] H. Yannon, D.R. Uhlmann, J. Non-Cryst. Solids 54 (1983) 253. [7] P.L. Lopez-Almany, J. Vazqez, P. Villares, R. Jimenez-Garay, J. Non-Cryst. Solids 287 (2001) 203. [8] A.A. Abu-Sehly, Physica B 325 (2003) 372. [9] A.A. Joraid, Physica B 390 (2007) 263. [10] A.A. Joraid, S.N. Alamri, A.A. Abu-Sehly, J. Non-Cryst. Solids 354 (2008) 3380. [11] S. Vyazovkin, N. Sbirrazzuoli, Macromol. Rapid Commun. 23 (2002) 766. [12] S. Vyazovkin, Macromol. Rapid Commun. 23 (2002) 771. [13] M.J. Starink, Thermochim. Acta 404 (2003) 163. [14] S. Vyazovkin, N. Sbirrazzuoli, Macromol. Rapid Commun. 27 (2006) 1515. [15] A.A. Joraid, Thermochim. Acta 456 (2007) 1. [16] H.L. Friedman, J. Polym. Sci. C 6 (1964) 183. [17] M.J. Starink, J. Mater. Sci. 42 (2007) 483. [18] B. Jankovic, B. Adnadevic, J. Jovanovic, Thermochim. Acta 452 (2007) 106. [19] H.E. Kissinger, J. Res. Nat. Bur. Stand. 57 (1956) 217. [20] H.E. Kissinger, Anal. Chem. 29 (1957) 1702. [21] T. Akahira, T. Sunose, Res. Rep. Chiba Inst. Technol. 16 (1971) 22. [22] J.H. Flynn, L.A. Wall, J. Res. Natl. Bur. Stand. Sect. A 70 (1966) 487. [23] T. Ozawa, Bull. Chem. Soc. Jpn. 38 (1965) 1881. [24] W. Tang, Y. Liu, H. Zhang, C. Wang, Thermochim. Acta 408 (2003) 39. [25] S. Vyazovkin, J. Comput. Chem. 18 (1997) 393. [26] S. Vyazovkin, J. Comput. Chem. 22 (2001) 178. [27] S. Vyazovkin, Anal. Chem. 74 (2002) 2749. [28] V.M. Gorbachev, J. Therm. Anal. 8 (1975) 349. [29] K. Matusita, T. Komatsu, R. Yokota, J. Mater. Sci. 19 (1984) 291. [30] A.A. Abu-Sehly, Thermochim. Acta 485 (2009) 14. [31] J.C. Fisher, D. Turnbull, J. Chem. Phys. 17 (1949) 71.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Structural and kinetic studies of crystallization of Te51 As42 Cu7 chalcogenide glass A.A. Abu-Sehly ∗,1 Physics Department, Faculty of Science, Taibah University, PO Box 344, Madina, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 9 May 2009 Received in revised form 17 June 2009 Accepted 18 June 2009 Available online 25 June 2009 PACS: 6470.P 6140 6140.D
a b s t r a c t Differential scanning calorimetry (DSC) technique was used to investigate the kinetics of crystallization in Te51 As42 Cu7 chalcogenide glass. Non-isothermal measurements were performed at different heating rates (2–99 K min−1 ). Two exothermic peaks were observed reflecting the presence of multiple phases in agreement with the structural investigation. A strong heating rate dependence of the activation energies associated with the two peaks was observed when the data were analyzed using Matusita model. This variation of the activation energy was confirmed by the application of the different isoconversional methods. These methods showed that the activation energy of crystallization is not constant but varies with temperature. Different temperature dependence of the activation energy was observed for the two crystallization peaks. © 2009 Elsevier B.V. All rights reserved.
Keywords: DSC Crystallization kinetics Chalcogenide glass Activation energy Isoconversional methods
1. Introduction Chalcogenide glasses have drawn a great attention during the last years. This is due to the fact that some amorphous materials show certain unusual switching properties that could be important in modern technological applications such as switching, electrophotography, and memory devices [1–4]. The system Te–As–Cu attracted considerable attention in the past because of the fact that addition of d-elements, such as Cu, to the chalcogenide glasses causes significant changes in their properties. This may reflect positively on their technological applications. The study of crystallization kinetics in amorphous materials by DSC methods has been discussed in many literatures [5–10]. There are several theoretical models and equations suggested to explain the crystallization kinetics. These models and equations will also be used for this study. Isoconversion methods are widely used to obtain reliable and consistent kinetic information from non-isothermal data. They can reveal the complexity of multiple reactions due to the dependence of the activation energy on the extent of conversion [10–14]. The kinetics of crystallization can be described by the following rate equation assuming Arrhenius temperature dependence of the
∗ Tel.: +966 508629110; fax: +966 48454770. E-mail address: [email protected]. 1 On leave from Physics Dept., Assiut University, Assiut, Egypt. 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.06.119
rate constant [14,15]:
d˛ E = A exp − RT dt
f (˛),
(1)
where t is the time, T is the temperature, ˛ is the conversion fraction that represents the volume of the crystallized fraction, A (s−1 ) is the pre-exponential (frequency) factor, E (kJ mol−1 ) is the activation energy, R is the universal gas constant, and f(˛) is the reaction model. Under non-isothermal conditions with a constant heating rate of ˇ = dT/dt, Eq. (1) may be rewritten as: d˛ d˛ = dT dt
1 ˇ
=
A E exp − RT ˇ
f (˛).
(2)
For various heating rates, ˇi , the Friedman method [16] can be obtained directly from Eq. (1) at a specific crystallization fraction, ˛, as: ln
d˛ dt
˛i
= CF (˛) −
E˛ , RT˛i
(3)
where the subscript i denotes different heating rates and the parameter CF (˛) = ln(A˛ f(˛)). For a specific ˛ value and several heating rates ˇi , pairs of (d˛/dt)˛i and T˛i are determined experimentally from the DSC thermograph. The parameters E˛ and CF (˛), at this specific value of ˛, are then estimated from a plot of ln(d˛/dt)˛i versus 1/T˛i (Eq. (3)) across at least three different heating rates. The procedure is repeated for many values of ˛, yielding continuous functions of ˛ for E˛ and CF (˛).
98
A.A. Abu-Sehly / Journal of Alloys and Compounds 486 (2009) 97–102
Eq. (2) can be integrated by separation of variables [17,18]:
˛
d˛ A = f (˛) ˇ
0
T
exp − T0
E RT
dT ≈
AE ˇR
0
T
exp(−y) dy, y2
(4)
where T0 is an initial temperature, y = E/RT and T is the temperature at an equivalent (fixed) state of transformation. The integral on the right hand side is usually called the temperature integral, P(y), and does not have analytical solution:
∞
exp(−y) dy. y2
P(y) = yf
(5)
To solve the temperature integral, several approximations were introduced. In general, all of these approximations lead to a direct isoconversion method in the form of
ln
ˇ
Tk
=C−
E . RT
(6)
For each degree of the conversion fraction, ˛, a corresponding k ) against 1/T . The T˛i and heating rate are used to plot ln(ˇi /T˛i ˛i activation energy, E˛ , is then determined from the regression slope. The most popular models used for calculation of activation energy are: (1) The Kissinger–Akahira–Sunose (KAS) method [19–21], which takes the form:
ln
ˇi
= CK (˛) −
2 T˛i
E˛ . RT˛i
E˛ , ln ˇi = CW (˛) − 1.0518 RT˛i
(8)
ln
1.894661 T˛i
E˛ = CT (˛) − 1.00145033 , RT˛i
(9)
(4) The Starink method [13,17], another new method, which is given by:
ln
ˇi 1.92 T˛i
= CS (˛) − 1.0008
˝=
n n I(E˛ , T˛i )ˇj i=1 j = / i
and
I(E˛ , T˛j )ˇi
I(E˛ , T˛i ) =
T˛i
exp 0
(3) The Tang method. A more precise formula for the temperature integral has been suggested by Tang et al. [24], which can be put in the form: ˇi
The third approach of extracting the same information is by using the advanced isoconversional method developed by Vyazovkin [14,25–27]. For a set of n experiments carried out at different heating rates, the activation energy can be determined at any particular value of ˛ by finding the value of E˛ which minimizes the objective function ˝, where:
(7)
(2) The Flynn–Wall–Ozawa (FWO) method, suggested independently by Flynn and Wall [22] and Ozawa [23]. This method is given by:
Fig. 2. Typical DSC trace of the Te51 As42 Cu7 chalcogenide glass heated at a constant rate of 15 K min−1 . The separation process for the first (P1) and second (P2) peaks was performed using Gaussian fit.
E˛ , RT˛i
Fig. 1. EDX results of the Te51 As42 Cu7 chalcogenide glass.
,
(11)
−E ˛
RT
dT.
(12)
The temperature integral, I, was evaluated using an approximation suggested by Gorbachev [28]:
T
exp 0
−E RT
dT =
RT 2 E
1 1 + (2RT/E)
exp
−E RT
.
(13)
The present study is concerned with the crystallization kinetics and the effect of temperature on the activation energy of Te51 As42 Cu7 chalcogenide glass by means of isoconversion meth-
(10)
Fig. 3. The XRD patterns of the as-prepared sample and of the annealed samples at different annealing temperature, Ta .
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temperature and enthalpy calibrations were checked with indium (Tm = 429.75 K, Hm = 28.55 J g−1 ) and tin (Tm = 504.97 K, Hm = 59.56 J g−1 ) as a standard material. The structure of the samples was examined using a Shimadzu XRD-6000 Xray diffractometer using CuK˛ radiation ( = 1.5418 Å). The X-ray tube voltage and current were 40 kV and 30 mA, respectively. The X-ray diffractometer was equipped with oven-chamber (Anton Paar HTK 1200N). The measurements were obtained at the annealing temperature. The surface microstructure was revealed by SEM (Shimadzu Superscan SSX-550), and the composition of the alloy was checked by EDX.
3. Results and discussion 3.1. Structural studies
Fig. 4. Electron microscopy patterns of Te51 As42 Cu7 chalcogenide glass as prepared in bulk specimen.
ods. The effect of annealing on the structure of the present sample was also investigated by SEM as well as by X-ray diffraction. 2. Experimental methods Bulk material was prepared by the well-established melt-quench technique. High purity (99.999%) Te, As and Cu in appropriate atomic percentage proportions were weighed and sealed in a quartz glass ampoule under a vacuum of 10−4 Torr. The contents were heated to about 1250 K for 36 h. During the melt process, the tube was frequently shaken to homogenize the resulting alloy. The melt was quenched in ice water to obtain the material in a glassy state. The DSC experiments presented in this paper were performed using a Shimadzu DSC-60 instrument with an accuracy of ±0.1 K, under dry nitrogen supplied at a rate of 35 ml min−1 . The samples were encapsulated in standard aluminum sample pans. To minimize the temperature gradients, the samples were well granulated to form a uniform fine powder and spread as thinly as possible across the bottom of the sample pan. The weight of the sample was kept very small (2–3 mg). Non-isothermal DSC curves were obtained at selected heating rates (ˇ in the range 2–99 K min−1 ). The
Qualitative and quantitative calculations were performed using the EDX technique accomplished with SEM from the displayed characteristic X-ray pattern. The results obtained are shown in Fig. 1. The atomic percentage ratios of Te, As and Cu were found to be 51%, 42% and 7%, respectively. Typical (DSC) curve is shown in Fig. 2. Two exothermic changes were observed: the first one (P1) was between 442 and 491 K for heating rates of 2–99 K min−1 , and the second (P2) from 493 to 534 K for the same heating rate range. The transformation from the amorphous to the crystalline state was investigated by X-ray diffraction measurements performed on sample heated at various temperatures 442, 468, 493, 513, 543 and 563 K. The XRD patterns are shown in Fig. 3. The as prepared sample was amorphous, as shown in Fig. 3. As the temperature increases the sharpness of the lines increases, indicating grain growth. The presence of a (1 1 2) as a main peak at 2 = 29.4◦ could be attributed to As2 Te3 [JCPDS file 75-1470]. There is a gradual phase change as the temperature goes up, but a remarkable change occurred at annealing temperature of 543 K where the peak (1 1 2) at 2 = 29.4◦ nearly disappeared and the peak (1 3 0) at 2 = 27.4◦ which could be attributed to Cu0.656 Te0.344 become the main peak [JCPDS file 37-1026]. The two binary crystalline phases Cu–Te and Cu–As were recognized at high temperatures as reported in our previous study
Fig. 5. Electron microscopy patterns of Te51 As42 Cu7 chalcogenide glass annealed for 15 min at different temperatures. (a) Annealed at 442 K, (b) annealed at 493 K, and (c and d) annealed at 513 K.
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[5], but with less broad composition ranges. The presence of the two peaks at 2 = 39.9◦ and 42.8◦ could be attributed to Cu2 Te[JCPDS files 45-1279 and 06-0649]. An evidence for the binary crystalline phase Cu–As is the presence of the peak at 2 = 37.9◦ which could be attributed to Cu9.5 As4 [JCPDS file 21-0280]. The transformation from the amorphous to the crystalline state was investigated by studying the morphology of the samples. The change in the morphology under isothermal annealing was recorded by SEM. Fig. 4 shows an SEM image of a fractured, as prepared, bulk specimen of Te51 As42 Cu7 . The micrograph shows the conchoidal contours, which are a good indication for glass structure. On the other hand, Fig. 5a–d shows the effect of heat treatments on the morphology under nitrogen flow. Fig. 5a shows an SEM micrograph of the Te51 As42 Cu7 sample after annealing for 15 min at 442 K. The micrograph indicates that the glass structure was distorted by the beginning of crystallization. It shows that the specimen consists of indistinct crystallites embedded in the original amorphous matrix. This distortion dramatically increases as temperature increases as shown in Fig. 5b for a sample annealed at 493 K for 15 min. By increasing the annealing temperature to 513 K for 15 min, a remarkable another phase of crystallization was developed. The crystalline phase appeared as an ordered pattern of very fine structure as shown in Fig. 5c and d. 3.2. The activation energy of crystallization The routinely and most widely used model is the Johnson–Mehl–Avrami (JMA) model for non-isothermal kinetics. This model implies that the Avrami exponent, n, and the activation energy, E, should be constant during the transformation process. Recent papers in this field have shown that n and E are not necessarily constants, but vary during the transformation [5,8–10]. The first step used in the calculation of the activation energy for crystallization is the separation of the processes for the first (P1) and second (P2) peaks by Gaussian fit as shown in Fig. 2. After this, each peak was treated individually. 3.2.1. Evaluation of the activation energy by the JMA model The kinetics of crystallization were obtained using a method specifically suggested for non-isothermal conditions by Matusita et al. [29] as: ln[− ln(1 − ˛)] = −n ln ˇ − 1.052
mE + constant, RT
(14)
where m is an integer which depends on the dimensionality of the crystal, and n is a numerical factor (the Avrami exponent) which also depends on the nucleation process. When the nuclei formed during the heating at a constant rate dominate, n = m + 1 and when nuclei formed during any previous heat treatment prior to thermal analysis are dominant, n = m [8]. In this work the values of the indices n and m are considered to be equal because the sample was pre-annealed for a period of time before each experimental run at a temperature below the glass transition temperature, Tg , thus ensuring that the site was saturated. The plot of ln[−ln(1 − ˛)] against 103 /T is shown in Fig. 6a and b. For both two peaks (P1) and (P2), the resulting straight lines in Fig. 6a and b have slopes that vary gradually with the heating rate. If the crystallization fraction, ˛, is determined at a fixed temperature, at different heating rates, then the Avrami exponent n can be obtained from the slope of the following equation [30]:
d{ln[− ln(1 − ˛)]} = −n. d(ln ˇ) T
(15)
The results are shown in Fig. 7a and b. The calculated values of n were not integers and varied with temperature as shown in Fig. 8. It is worth noting that for P1 the value of n is constant (n ≈ 1) for
Fig. 6. (a) ln[−ln(1 − ˛)] versus 1/T plot at different heating rates for the first peak (P1) of the Te51 As42 Cu7 chalcogenide glass. (b) ln[−ln(1 − ˛)] versus 1/T plot at different heating rates for the second peak (P2) of the Te51 As42 Cu7 chalcogenide glass.
temperatures up to 480 K indicating that the crystallization is dominated by surface morphology. The gradual increase of the values of n for P2 is an indication of changing morphology of the crystallization process from surface (n = 1) to layer (n = 2) structures. This change of morphology with temperature is also evident from Fig. 5b and c, respectively. Fig. 9 shows the variation of the activation energy for crystallization with the heating rate for an average value of n = 1.11 and 1.38 for P1 and P2, respectively obtained from the results. The results show that the activation energy decreases with heating rate more rapidly for P1 than P2. 3.2.2. Evaluation of the activation energy by isoconversional methods The first step in the evaluation of the activation energy for crystallization, E˛ (T), is to apply the isoconversional methods mentioned in Eqs. (3) and (7)–(11) to the overall crystallization data to obtain the dependence of E˛ (T) on ˛ for all heating rates applied. The dependence of E˛ on the temperature can be obtained [15] by replacing ˛ with the respective temperature interval. Fig. 10 shows the dependence of E˛ on the volume fraction crystallized, ˛, for P1 and P2 transformations. The results are obtained by applying the six isoconversional methods of Friedman, KAS, FWO, Tang, Starink and Vyazovkin given in Eqs. (3) and (7)–(11), respectively. The results obtained by the KAS, FWO, Tang, Starink and Vyazovkin methods were well matched and gave identical values while the results obtained by the Friedman method gave dif-
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Fig. 9. Effective activation energy (E) as a function of heating rate for the two crystallization peaks of the Te51 As42 Cu7 chalcogenide glass.
Fig. 7. (a) ln[−ln(1 − ˛)] versus ln(ˇ) plot at different temperatures for the first peak (P1) of the Te51 As42 Cu7 chalcogenide glass. (b) ln[−ln(1 − ˛)] versus ln(ˇ) plot at different temperatures for the second peak (P2) of the Te51 As42 Cu7 chalcogenide glass.
Fig. 10. Dependence of the activation energy for crystallization, E, on the volume of the crystallized fraction, ˛, for the two crystallization peaks.
ferent values. This shift is known and has been discussed for other compounds [9,15]. For P1 the results show that E˛ first decreases rapidly with the extent of conversion, ˛, then, in the conversion range of ˛ > 0.9, E˛ increases for results obtained by Eqs. (7)–(11). Friedman method showed that E˛ started to increase more earlier with the extent
of conversion, at ˛ > 0.7. For P2 the results show that E˛ is nearly constant with the extent of conversion, ˛, with exception at the beginning of crystallization (˛ < 0.2) where E˛ is decreasing. The occurrence of the dependence of E˛ on the volume of the crystallized fraction instantly suggests that the data under study follow
Fig. 8. The variation of the Avrami exponent, n, with temperature for the two crystallization peaks.
Fig. 11. Dependence of the activation energy for crystallization, E, on temperature for the two crystallization peaks.
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a multi-step kinetics reaction for P1, while mainly they follow a single-step kinetics reaction for P2. The resulting E˛ (T) dependence as obtained from Eqs. (3) and (7)–(11) is displayed in Fig. 11 for both peaks P1 and P2. For P1 the values of E˛ are positive and decrease with temperature for the six methods used, which simply indicates that the crystallization rate increases as the temperature increases. This behavior demonstrates that the rate of crystallization is, in fact, determined by the rates of the nucleation and diffusion processes [13]. Because these two mechanisms are likely to have different activation energies, the effective activation energy of the transformation will vary with temperature [30]. This interpretation is based on the nucleation theory proposed by Fisher and Turnball [31]. 4. Conclusion The structure and kinetics of crystallization of Te51 As42 Cu7 were investigated. The X-ray diffraction measurements confirmed the presence of different phases as the samples were annealed at different temperature. Different crystalline structures can also be seen from the morphology of specimens annealed at selected stages of heat treatments. Two exothermic peaks were observed reflecting the presence of multiple phases in agreement with the structural results. The activation energies of crystallization, E(T), were estimated by applying different isoconversional methods and were found to be strongly temperature dependent. The results showed a decrease followed by an increase in E(T) with increasing temperature for P1, while for P2, it increases with increasing temperature then followed by a decrease. The observed temperature dependence of E can be understood on the light of the nucleation theory of Fisher and Turnball.
References [1] T. Ohta, J. Optoelectron. Adv. Mater. 3 (2001) 609. [2] S.A. Khan, M. Zulfequar, M. Husain, J. Phys. Chem. Solids 63 (2002) 1787. [3] M. Popescu, J. Optoelectron. Adv. Mater. 7 (2005) 2189. [4] N. Mehta, J. Sci. Ind. Res. 65 (2006) 777. [5] A.A. Joraid, A.A. Abu-Sehly, M. Abu El-Oyoun, S.N. Alamri, Thermochim. Acta 470 (2008) 98. [6] H. Yannon, D.R. Uhlmann, J. Non-Cryst. Solids 54 (1983) 253. [7] P.L. Lopez-Almany, J. Vazqez, P. Villares, R. Jimenez-Garay, J. Non-Cryst. Solids 287 (2001) 203. [8] A.A. Abu-Sehly, Physica B 325 (2003) 372. [9] A.A. Joraid, Physica B 390 (2007) 263. [10] A.A. Joraid, S.N. Alamri, A.A. Abu-Sehly, J. Non-Cryst. Solids 354 (2008) 3380. [11] S. Vyazovkin, N. Sbirrazzuoli, Macromol. Rapid Commun. 23 (2002) 766. [12] S. Vyazovkin, Macromol. Rapid Commun. 23 (2002) 771. [13] M.J. Starink, Thermochim. Acta 404 (2003) 163. [14] S. Vyazovkin, N. Sbirrazzuoli, Macromol. Rapid Commun. 27 (2006) 1515. [15] A.A. Joraid, Thermochim. Acta 456 (2007) 1. [16] H.L. Friedman, J. Polym. Sci. C 6 (1964) 183. [17] M.J. Starink, J. Mater. Sci. 42 (2007) 483. [18] B. Jankovic, B. Adnadevic, J. Jovanovic, Thermochim. Acta 452 (2007) 106. [19] H.E. Kissinger, J. Res. Nat. Bur. Stand. 57 (1956) 217. [20] H.E. Kissinger, Anal. Chem. 29 (1957) 1702. [21] T. Akahira, T. Sunose, Res. Rep. Chiba Inst. Technol. 16 (1971) 22. [22] J.H. Flynn, L.A. Wall, J. Res. Natl. Bur. Stand. Sect. A 70 (1966) 487. [23] T. Ozawa, Bull. Chem. Soc. Jpn. 38 (1965) 1881. [24] W. Tang, Y. Liu, H. Zhang, C. Wang, Thermochim. Acta 408 (2003) 39. [25] S. Vyazovkin, J. Comput. Chem. 18 (1997) 393. [26] S. Vyazovkin, J. Comput. Chem. 22 (2001) 178. [27] S. Vyazovkin, Anal. Chem. 74 (2002) 2749. [28] V.M. Gorbachev, J. Therm. Anal. 8 (1975) 349. [29] K. Matusita, T. Komatsu, R. Yokota, J. Mater. Sci. 19 (1984) 291. [30] A.A. Abu-Sehly, Thermochim. Acta 485 (2009) 14. [31] J.C. Fisher, D. Turnbull, J. Chem. Phys. 17 (1949) 71.